Solve {l}{x=4(y+z)}{x-y=2}{x+y+z=5}

$$\left. \begin{array} { l } { x = 4 ( y + z ) } \\ { x - y = 2 } \\ { x + y + z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x=4$$

$$y=2$$

$$z=-1$$

Short Steps Using Substitution

Calculate x from x=4\left(y+z\right).

$$x=4y+4z$$

Substitute 4y+4z for x in the second and third equation.

$$4y+4z-y=2 4y+4z+y+z=5$$

Solve these equations for y and z respectively.

$$y=\frac{2}{3}-\frac{4}{3}z z=1-y$$

Substitute \frac{2}{3}-\frac{4}{3}z for y in the equation z=1-y.

$$z=1-\left(\frac{2}{3}-\frac{4}{3}z\right)$$

Solve z=1-\left(\frac{2}{3}-\frac{4}{3}z\right) for z.

$$z=-1$$

Substitute -1 for z in the equation y=\frac{2}{3}-\frac{4}{3}z.

$$y=\frac{2}{3}-\frac{4}{3}\left(-1\right)$$

Calculate y from y=\frac{2}{3}-\frac{4}{3}\left(-1\right).

$$y=2$$

Substitute 2 for y and -1 for z in the equation x=4y+4z.

$$x=4\times 2+4\left(-1\right)$$

Calculate x from x=4\times 2+4\left(-1\right).

$$x=4$$

The system is now solved.

$$x=4 y=2 z=-1$$